Precalculus (6th Edition) Blitzer

Published by Pearson
ISBN 10: 0-13446-914-3
ISBN 13: 978-0-13446-914-0

Chapter 1 - Section 1.4 - Linear Functions and Slope - Exercise Set - Page 213: 71

Answer

$x=-3/2$, $y=-6$, see graph

Work Step by Step

Consider the given linear equation $8x-2y+12=0$ Use intercepts to graph the given equation as follows: Step 1: Find the $x$ intercept. To calculate the x intercept of the line, substitute $y=0$ in the equation and find the value of x. $\begin{align} & 8x-2\times 0+12=0 \\ & 8x=-12 \\ & x=\frac{\left( -12 \right)}{8} \\ & =-1.5 \end{align}$ So, the $x$ intercept of the given equation $8x-2y+12=0$ is $-1.5$. Hence, the line passes through the point $\left( -1.5,0 \right)$. Step 2: Find the $y$ intercept. To calculate the y intercept of the line, substitute $x=0$ in the equation and find the value of y. $\begin{align} & 8\times 0-2y+12=0 \\ & -2y=-12 \\ & y=\frac{\left( -12 \right)}{\left( -2 \right)} \\ & =6 \end{align}$ So, the $y$ intercept of the equation $8x-2y+12=0$ is 6. Hence, the line passes through the point $\left( 0,6 \right)$. Step 3: Plot the graph the equation of the straight line. Locate the two intercepts $\left( -1.5,0 \right)$ and $\left( 0,6 \right)$. Connect them by a straight line. The graph of the given equation $8x-2y+12=0$ is as follows:
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